Answer to Question #131702 in Microeconomics for Zarwar

Question

What is meant by an expansion path? Illustrate expansion paths for a normal input and an inferior input.

Answer 1

Expansion path is a graph that traces all points of tangency between the isocost lines and isoquants, and shows changes in the firm's cost minimizing input mix as production expands. The path is also known as the scale line as it connects all optimal input combinations of labour and capital as the scale of production expands. Thus, the path describes how the optimal input combinations of labour and capital increases in response to an increase in production, holding input prices constant. This means that if labour and capital are the only production inputs, then the expansion path describes the optimal or equilibrium capital-labour ratio.

The expansion path is also useful in describing the nature of the firm's inputs and classifies them into normal inputs and inferior inputs.

A normal input is an input in which a firm increases its proportion in the production mix as production expands. The expansion path slopes upwards as input proportion and production are positively related. The gragh below describes a normal input.

As shown above, the path connects all points of tangency between isocost lines (ICs) and isoquants (IQs). The proportion of labour and capital remains unchanged as production expands. Labour and capital are both proportionately increased along with production. Both inputs are therefore normal inputs and, as shown above, the path slopes upwards.

An inferior input is an input whose proportion decreases as production expands. This is because the firm switches to other inputs that are more productive, at higher production levels. The expansion path, thus, slopes away from an inferior input, that is, it has a negative slope. This is shown on the graph below.

As show on the gragh above, the proportion of labour decreases as production expands. Capital is substituted in place of labour as production expands. This is because with the expansion of production, as scale increases, capital becomes more productive than labour and hence the firm switches from labour to capital. The path thus slopes away from labour, hence becomes negatively sloped as shown. Labour is thus an inferior input.